Real were missing injured top scorer Cristiano Ronaldo for their second La Liga outing of the campaign but quickly went 2-0 ahead at the Anoeta in San Sebastian before losing control of the match and crashing to a 4-2 reverse.
"The team was negative in everything, horrible, we did not play well," Casillas told reporters.
"We cannot let a match get away from us in that way after leading 2-0," added the Spain international.
"This is not the attitude or the way to go. We are wearing a very important badge on our chests and this is not the example we should be giving.
"We have to accept the defeat and learn from today's mistakes."
Real's reverse will set alarm bells ringing among fans concerned that the sale of the experienced Xabi Alonso to Bayern Munich last week has left the team exposed in midfield.
Coach Carlo Ancelotti said the problem on Sunday was not the absence of one player but a generally poor attitude.
New arrivals such as Germany midfielder Toni Kroos and Colombia playmaker James Rodriguez needed more time to adapt, the Italian added.
"In matches like today's it is more difficult for the newcomers," Ancelotti told a news conference.
"The first 30 minutes were very good, with quality, pace and focus. The rest was very bad.
"It is difficult to explain what happened. We conceded corners, free kicks.
"We're very sorry, I don't like the team to play like that for an hour. The first half an hour was very good, but we have to think and change this."
Casillas singled out poor defending at set pieces as a particular problem and said the team needed to be more alert at corners and free kicks.
"We were making mistakes throughout the whole game and that's why they put four goals past us," he added.
"We had very clear scoring chances but later we did not defend. We have to up the pressure and be more alert
"We are all to blame, not just the defence, because everyone is back defending at a corner. We have to sort it our because what happened is not normal."